Sequences & series worksheet with answers

Free printable Sequences & series worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
kak​123456789101112

The arithmetic sequence 20, 16, 12, 8, … ends with the term −120. How many terms n does it have?

a₁ = 20d = −4aₙ = −120
n =
2.Easy
kak​123456

Find the sum S6 of the first 6 terms of the geometric sequence 1, −2, 4, …

a₁ = 1r = −2n = 6
S6 =
3.Medium
AΣ (5/3)ᵏk = 1 … ∞BΣ 5/k²k = 1 … ∞CΣ (−1)ᵏ/kk = 1 … ∞DΣ 3ᵏ/k!k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ (5/3)ᵏB: Σ 5/k²C: Σ (−1)ᵏ/kD: Σ 3ᵏ/k!
  1. 1A: Σ (5/3)ᵏ
  2. 2B: Σ 5/k²
  3. 3C: Σ (−1)ᵏ/k
  4. 4D: Σ 3ᵏ/k!
4.Medium
k|aₖ|¹ᐟᵏ123456789101112

Apply the root test to Σk=1∞ ((3k + 2)/(2k + 5))ᵏ. Find L = lim |ak|1/k.

ak = ((3k + 2)/(2k + 5))ᵏ
L =
5.Hard

f(x) = sin x is approximated by its Maclaurin polynomial of degree 2 at x = 0.2. Use the Lagrange error bound M·|x|ⁿ⁺¹/(n + 1)! with M = 1 to find the largest possible error |R₂|.

f(x) = sin xn = 2x = 0.2M = 1
|R₂| =
6.Hard
xyfP₄0.5

Use the Maclaurin polynomial of degree 4 of f(x) = cos(3x) to approximate f(0.5). Give P₄(0.5).

f(x) = cos(3x)n = 4x = 0.5
P₄(0.5) =

Answer key

  1. 1. n = 36
  2. 2. S6 = −21
  3. 3. A: Σ (5/3)ᵏ
  4. 4. L = 1.5
  5. 5. |R₂| = 0.001333
  6. 6. P₄(0.5) = 0.08594

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